arXiv subjects

H. Weigel

Publications and source records attributed to H. Weigel.

114 records · Page 7Linked to original sources

arXiv1993

$1/N_C$ Corrections to $g_A$ in the Light of PCAC$

We comment on recently discovered $1/N_C$ corrections to the ` nucleon axial current in the framework of the Nambu--Jona-Lasinio soliton. This kind of corrections arises only for a special treatment of ordering ambiguities of collective coordinates and operators in the semiclassical quantization. In addition to the missing derivation of this special quantization scheme from first principles its na\"ıve application violates partial conservation of the axial current (PCAC). We show how within this scheme PCAC can be restored and determine the corresponding $1/N_C$ corrections to the equation of motion for the chiral soliton. The resulting self-consistent solution allows to evaluate the nucleon axial coupling constant $g_A$ directly as a matrix element of the axial current as well as indirectly from the pion profile function. Enhancement is found for those baryon properties which are sensitive to the long range behavior of the pion profile.

hep-ph↗

arXiv1993

The Nambu-Jona-Lasinio Chiral Soliton with Constrained Baryon Number

A regularization for the baryon number consistent with the energy in the Nambu-Jona-Lasinio model is introduced. The soliton solution is constructed with the regularized baryon number constrained to unity. It is furthermore demonstrated that this constraint prevents the soliton from collapsing when scalar fields are allowed to be space dependent. In this scheme the scalar fields actually vanish at the origin reflecting a partial restoration of chiral symmetry. Also the influence of this constraint on some static properties of baryons is discussed.

hep-ph↗

arXiv1993

Strange and Non-Strange Meson Fluctuations off the Nambu--Jona-Lasinio Soliton

Mesonic fluctuations off the chiral soliton of the Nambu--Jona-Lasinio model are investigated. The hedgehog configuration is proven to represent a local extremum of the action. The method is applied to flavor SU(3) and the energy eigenvalue of the kaon bound state in the soliton background is evaluated which is the key ingredient for the Callan-Klebanov approach to hyperons. The energy eigenvalue of the corresponding strange-valence-quark is found to be 183MeV higher than the energy eigenvalue of the up-valence-quark when 400MeV is assumed for the up-quark constituent mass.

hep-ph↗

arXiv1993

The Chiral Soliton of the Nambu Jona-Lasinio Model with Vector and Axial Vector Mesons

The self-consistent chiral soliton of the Nambu--Jona-Lasinio model including the $ω,ρ$ and $a_1$ (axial-) vector meson fields besides the chiral angle is investigated. The resulting energy spectrum of the one particle Dirac Hamiltonian is strongly distorted leading to a polarized Dirac sea which carries the complete baryon number. This supports Witten's conjecture that baryons can be described as topological solitons. The exploration of the isoscalar mean squared radius of the nucleon exhibits that the repulsive character of the isoscalar vector field $ω$ as well as the attractive features of the (axial-) vector mesons $ρ$ and $a_1$ are reproduced in the Nambu--Jona-Lasinio model. The axial charge of the nucleon $g_A$ comes out far too small. This can be understood as an artifact of the proper time regularization prescription.

hep-ph↗

arXiv1992

Vector mesons in the collective approach to SU(3)

We study the SU(3) extension of the Skyrme model with vector mesons in the collective quantization scheme. The parameters of the model are fixed in its mesonic sector. Fields which are excited by the collective rotation of the classical soliton are determined by a variational method. The resulting collective Hamiltonian which includes various symmetry breaking terms is diagonalized exactly. This yields reasonable predictions for the mass differences of the low-lying baryons. We furthermore investigate static properties of these baryons in this model by evaluating all relevant matrix elements using the exact eigenstates of the collective Hamiltonian. Electromagnetic observables are found to approximately obey the predictions obtained from SU(3) symmetry. Strong deviations from SU(3) symmetry are, however, found for the matrix elements of strange vector and scalar operators indicating a small amount of strangeness in the proton. The exploration of axial currents shows that the results of the EMC experiment may be explained with a small polarization of the strange sea of the proton without violating the successful Cabibbo model for semileptonic hyperon decays.

hep-ph↗

arXiv1992

Effective Hadron Dynamics: From Meson Masses to the Proton Spin Puzzle

We construct a three flavor chiral Lagrangian of pseudoscalars and vectors with special emphasis on the symmetry breaking terms. Comparing tree level two and three point functions with experiment allows us to first, fix the parameters of the model (including the light quark mass ratios) and second, to predict $m(K^{*+})-m(K^{*\circ}),\, Γ(K^*\rightarrow Kπ)$ and $Γ(ϕ\rightarrow K {\overline K})$. The last mentioned quantities come out reasonably well, in contrast to an ``ordinary" $SU(3)$ treatment. For this purpose we need ``second order" symmetry breakers involving the vector fields analogous to those needed for the chiral perturbation theory program with only pseudoscalars. An improved description of the $η-η^\prime$ system is also given. We then use the soliton sector of this improved chiral Lagrangian to investigate some aspects of baryon physics which are especially sensitive to symmetry breaking. For this purpose a fairly elaborate ``cranking" techinque is employed in connection with the collective Hamiltonian. In addition to the ``strong" baryon mass spectrum a careful investigation is made of the non-electromagnetic part of the neutron-proton mass difference. This work is needed to improve our previous estimates concerning the two component approach to the ``proton spin" puzzle. We find that both the ``matter" and ``glue" contributions are small but they do tend to cancel each other.

hep-ph↗